n
67
Unrestricted weight-6 CSS cell. The priced construction calculus was applied one move deep to every CSS entry on the board, and this code is the E-PEEL of codes/68-6-5.json ([[68,6,5]], max check weight 5; itself Mathys Rennela's priced-calculus E-PEEL of codes/70-6-5.json, a two-block group-algebra code over C35 from arXiv:2610.13880). Peeling qubit 14 with the one Z check that touches it keeps k = 6 and keeps the witnessed distance bound at 5 while dropping one qubit. Max check weight stays 5.
Every C-DELETE-CHECK, E-PEEL, and E-PUNCTURE move on each of the 2,783 CSS board entries as of 2026-11-02, 1,684,787 moves in all, with the consumer at github.com/unitaryfoundation/code-calculus @ 1b9a942. Children with a bare qubit, a disconnected Tanner graph, a Weisfeiler-Leman signature equal to a board entry or to an earlier child, or parameters already dominated inside the parent's cell were dropped before any search, leaving 334,191 distinct children. Children with n <= 60 and an inherited distance bound of at least 2, and children with 61 <= n <= 100 and a bound of at least 5, were screened with research/kit/surrogate.lightest_logical at 2,000 RIS trials per side; the survivors the kit's novelty pre-check called board-advancing were staged with research/kit/submit.py and gated with verify/validate_candidate.py, one representative per distinct (n, k, d, max weight, locality) point. This code is that representative for [[67,6,5]] at max check weight 5. The thirteen points audited first went to the board on 2026-11-04 (PRs #4588 to #4600); this one is from the remainder, re-checked against the board of 2026-11-04 with the gate's structural, deduplication, and novelty stages before the ladder below was run. The screen distance is a witness-backed upper bound; the rungs below are the independent confirmation runs on the staged file.
Confirmation ladder for the submitted code, each rung a fresh seed unless marked otherwise, reading the lightest logical found:
| budget (trials/side) | lightest logical | | ---: | ---: | | 2,000 (staging screen, seeds 1 and 2) | 5 | | 1,000,000 (seed 101) | 5 | | 1,000,000 (seed 102) | 5 | | 10,000,000 (seed 103) | 5 |
4 fresh-seed rung(s) agree at the best bound, the deepest of them at 10,000,000 trials per side. The submitted witness reproduces it: X: d <= 5 (upper_bound), Z: d <= 5 (upper_bound).
None recorded for this candidate.
Model: Claude Fable 5.1 (Claude Code). Repo tooling: research/kit/coordination.py, research/kit/submit.py, research/kit/surrogate.py, research/audits/leader_audit.py. The local verdict is verify/validate_candidate.py; the bundle was assembled by research/kit/promote.py.
Load codes/68-6-5.json, delete qubit 14 (0-based index in that file) together with its unique Z check b15, where the Z rows are numbered b1, b2, ... in file order after dropping rows dependent on earlier ones, as CodeState.from_challenge in machine/priced_calculus.py labels them, and relabel the surviving qubits in increasing order of their parent indices; in github.com/unitaryfoundation/code-calculus @ 1b9a942 this is apply_operation(state, {'op': 'E-PEEL', 'qubit': 14, 'sector': 'Z', 'row_id': 'b15'}). Then run research/audits/leader_audit.py ladder on the result with --ladder 1000000:101,102 10000000:103 to reproduce the confirmation rungs; the witnesses in the entry are the ones those runs validated.